Liberal senator Lucy Gichuhi backflips on naming bullies

Liberal senator Lucy Gichuhi has told Scott Morrison she was not bullied in connection with the party's messy leadership contest.

The South Australian senator had threatened to use parliamentary privilege to publicly out colleagues accused of bullying and intimidation during last month's Liberal leadership crisis.

But Mr Morrison said Senator Gichuhi has told him the leadership was not at the heart of the issue.

"She made it very clear to me that in terms of the events in Canberra, and the spill of the leadership, she told me very plainly that she was not bullied by anybody here in Canberra in relation to that matter," he told ABC TV on Tuesday.

The prime minister said there are other issues at play, including how party divisions are handled, but that gender has not been a factor in people's behaviour and he hasn't been provided with names.

"There was no sort of gender-specific actions that related to what some would call very intense lobbying, which is fairly normal in the political process, albeit not edifying," he said.

Asked earlier by Labor whether he or the party whips were in charge of complaints handling, Mr Morrison said he took a "keen interest" in the welfare of all his coalition colleagues.

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A spokesman for Senator Gichuhi told AAP she has left the prime minister to deal with the issue, so she will not be naming those she accuses of bullying.

"Regarding bullying in my political career: Yesterday I had a discussion with Prime Minister Scott Morrison. The Prime Minister has taken up the issue," Senator Gichuhi posted to Twitter on Tuesday.

"We must live and work in a way that respects and enhances ALL freedoms of ALL Australians. Australia says NO to bullying and intimidation."

In the Senate, cabinet minister Mathias Cormann said he and the prime minister engaged with colleagues such as Senator Gichuhi "on a regular basis".

"We're not going to start putting private conversations on the floor of the Senate, but every individual senator of course is able to express their views in relation to their own circumstances as they see fit," Senator Cormann said.

Asked whether bullying occurred during the Liberal leadership struggle, Senator Cormann said: "We do work in a particular workplace where exchanges of views and seeking to convince each other of the merits of our arguments on policy and personnel is part of our core business. From time to time we go through difficult periods."